The most common and most likely answer to this crossword clue is the 5 plus 9 plus 9 letter word PARTY POLITICAL BROADCAST
I've seen this crossword clue in The Times
P
A
R
T
Y
P
O
L
I
T
I
C
A
L
B
R
O
A
D
C
A
S
T
Buddy explains!
The straight part
We know that "TV ad that'll cause some to switch over to the other side" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tv ad that'll cause some to switch over to the other side = party political broadcast.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.